## Research Abstracts Online

January 2010 - March 2011

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### University of Minnesota Twin Cities

College of Science and Engineering

School of Mathematics

# PI: Panagiotis Stinis

### Reduced Order Modeling for the Three-Dimensional Euler Equations

Fluid flows are ubiquitous in nature. They are complex, fascinating, and increasingly important in many areas ranging from biological flows to interstellar explorations. Most fluid flows of practical interest have one common feature: they are more complex than can be handled with state of the art mathematical tools and existing computational power. Moreover, even if one could reproduce them, real-world flows would entail a tremendous amount of data, while at the same time many quantities of interest would only be coarse-scale features. Thus, a more modest and at the same time more ambitious goal is to try to construct better (computational) reduced models for fluid flows which will be able to predict accurately the salient features of the flow. Recent work by these researchers has shown that it is possible to construct reduced models for the fluid flow equations starting from the equations themselves, i.e. without the incorporation of extra terms by hand as is done for example in regularization approaches. The goal of the current research project is to study in more detail the proposed reduced models. The simplest framework in which to study these models is that of homogeneous isotropic turbulence. The insights acquired from this project will help elucidate the problem of how (and how fast) energy cascades to smaller scales in fluid flows. In turn this can lead to a better modeling procedure for realistic flows.

### Group Member

Andrew Aspden, High Performance Computing Research, Lawrence Berkeley National Laboratory, Berkeley, California